Perfect beautiful girl who actually isn't at fault at all, she's just made out to be bad. Screams Mary Sue to me.

Quoting from the wiki page:

A Mary Sue (sometimes just Sue), in literary criticism and particularly in fan fiction, is a fictional character with overly idealized and hackneyed mannerisms, lacking noteworthy flaws, and primarily functioning as a wish-fulfillment fantasy for the author or reader. It is generally accepted as a character whose positive aspects overwhelm their other traits until they become one-dimensional. While the label "Mary Sue" itself originates from a parody of this type of character, most characters labelled "Mary Sues" by readers are not intended by authors as such. Male Mary Sues are often dubbed "Gary Stu", "Larry Stu", "Marty Stu", or similar names.

Perfect beautiful girl who actually isn't at fault at all, she's just made out to be bad. Screams Mary Sue to me.

Quoting from the wiki page:

A Mary Sue (sometimes just Sue), in literary criticism and particularly in fan fiction, is a fictional character with overly idealized and hackneyed mannerisms, lacking noteworthy flaws, and primarily functioning as a wish-fulfillment fantasy for the author or reader. It is generally accepted as a character whose positive aspects overwhelm their other traits until they become one-dimensional. While the label "Mary Sue" itself originates from a parody of this type of character, most characters labelled "Mary Sues" by readers are not intended by authors as such. Male Mary Sues are often dubbed "Gary Stu", "Larry Stu", "Marty Stu", or similar names.

I mean her whole schick is that she is Perfect at Everything. It's pretty much the main plot device of the series.

In fact I think her superpower has officially been described as what ever ability she encounters in an opponent she gains it and comes up with a perfect version of it.

She is, but probably in the same vein that the original Mary Sue was, rather than the characters Mary Sue was parodying that came to be known as "Mary Sues" in homage to the character that pointed out how bad the other star trek fan fiction writers characters were . The character Mary Sue from the original fan fic that the term was coined from, was intentionally made to be ridiculously characterized as she, as well as the story she was in, were making fun of most of the other star trek fan fiction of the time. Medaka being intentionally overpowered and ridiculous intentionally rather than as a form of wish fulfillment of the author makes her more akin to the original Mary Sue than the characters that became referred to as Mary Sues, especially since she is intentionally and with writer awareness made extremely absurd as a gimmick. Its also kind of important as the POV of Medaka Box is not from Medaka's point of view, as Mary Sues generally are, not to mention that Medaka has a big flaw in the fact she can be provoked to extreme unempathetic violence should she be pushed to far, which runs contrary to her normal portrayal as being practically perfect.

"Mary Sues" as the term originally was meant are characters that are functionally wish fullfillment by the author, where they basically insert an over idealized version of what they would want to be like themselves if they were in the stories world,. Mary Sue was created to make fun of all of the fanfiction written by women who made ST fanfic characters that were not only special snowflakes, but special snowflakes on every level to the point they were implausible. They were half Vulcan, youngest of their class with the highest grades, master engineer, combatant, medical doctors, that all bagged Captain Kirk and made him think of no other women, while saving the entire federation with a heroic sacrifice that fundamentally changed the way all of alien culture thinks, and with only flaws that serve to make them more special(I am the bastard child of the King type of flaws.). But the important part about them being Mary Sue's is that this is all wrapped up in one character, and its played straight rather than being played for intentional absurdity, because the author is to busy fulfilling their own empowerment fantasies through the character.

Most people today use the term Mary Sue in a random haphazard way however to either describe some character they don't like, or mislabel someone that is "perfect" in a few ways rather than all ways, or that is overpowered but with flaws, rather than its intended usage of a character that is literally the best at everything with no impactful flaws, as well as having the universe revolve around them and universally loved by everyone.

I'm sure there are some Mary Sue's in anime but they aren't usually anywhere as common as in fan fics, as actual successful writers tend to be able to avoid such glaring pitfalls, and I can't currently can't think of one that is a perfect example.

Even characters such as say Belldandy from AMG, don't really qualify as Mary Sue's since, despite her being an extremely powerful entity with an idealized personality, her character sticks with the few things about her that makes her special rather than trying to throw the kitchen sink of other things to make her more special for the hell of it. If she was the Mary Sue of the story she would have to be the Half demon and not Urd no matter how pointless it would be, as Mary Sues do not allow for other characters to share the spotlight. Her flaws are also rather mundane in her naivety and repressiveness of her own feelings in order to put others first, rather than more outlandish ones that serve only to make her more "unique".